We have the following proposition: $$P(n): 13^n+7^n-2\vdots 6$$.
- Prove $P(n)$ in two ways. I know that one of them is mathematical induction. I don't know many things about the other one, I know it's something from modular arithmetic.
- If we had $p_n = 13^n+7^n-2$ with $n\in\Bbb N^*$, how should we calculate the rest of $p_n:6$?